Cryptography Reference
In-Depth Information
Alice's Faraday rotator. Using Faraday rotation as an example, the AWI asso-
ciates the single-photon transformation
H
in
→
V
out
V
in
→
H
out
(10.1)
with the two-photon state
(10.2)
In going from Equation (10.1) to Equation (10.2), the propagation direction
for
H
in
and
V
in
is reversed. To preserve the handedness of the coordinate
system, one of the transverse directions must be reversed as well. This may be
accomplished by replacing
V
in
with
|
H
in
V
out
+|
V
in
H
out
.
V
in
. Thus we see that the AWI associates
Faraday rotation with the polarization singlet state
−
|
HV
−|
VH
.
10.2.2 One-Way Noise-Immune
Polarization-Coded QKD
We arrive at the one-way scheme of Figure 10.1(B) by “folding” the input
arm of the Faraday rotator of Figure 10.1(A) along the dashed line, thereby
replacing a round-trip single-photon space-time diagram with a one-way,
two-photon space-time diagram (the dotted line connecting the two photons
indicates entanglement). What follows is a passive-detection version of the
three-photon scheme presented in Reference [3]. Alice sends three photons
to Bob, with the first two (case 1), the last two (case 2), or the first and last
(case 3) in the singlet state and the other photon unpolarized. Bob makes his
measurements using the passive setup shown on the right side of Figure 10.2.
By appropriate postselection, this setup effectively makes a random choice
of two out of the three photons and brings them together on a nonpolarizing
beam splitter, which serves to distinguish the singlet state from the other three
Bell states [12]. Ignoring the first Mach-Zehnder interferometer (with relative
Alice
Bob
τ
4
τ
τ
Figure 10.2
A schematic of one-way noise-immune polarization-coded QKD [see
Figure 10.1(B)]. Alice sends three photons to Bob, with the first two (case 1), the last
two (case 2), or the first and last (case 3) in the singlet state and the other photon unpo-
larized. The delay in Bob's first and second interferometer are 4
, respectively.
Bob's apparatus effectively makes a random choice of two out of the three photons and
brings them together on a nonpolarizing beam splitter, which serves to distinguish
the singlet state from the other three Bell states [12]. The operation of the protocol is
described in the text.
τ
and
τ
